Various electronic applications exist that involve sending varying currents through a circuit and then reading and recording the output voltage that corresponds to each current. In many cases, this output voltage is the base-emitter voltage, a p-n junction, of a bipolar junction transistor (BJT). One such circuit is an electronic temperature sensor circuit that is configured to measure the temperature on a remote (separate) silicon chip by providing two target collector currents (IC1, IC2) to a p-n junction located on the remote chip. This circuit measures two diode voltages (VBE1, VBE2) of this p-n junction and processes the diode voltages to determine the actual temperature at the remote location. Most p-n junctions employed for this purpose are parasitic vertical p-n-p silicon based transistors. Also, the temperature sensor circuit is usually arranged to control the emitter currents of the transistor.
The classic diode equation determines a change in the base emitter voltage (ΔVBE) for a p-n-p transistor as follows:
                              Δ          ⁢                                          ⁢          Vbe                =                  η          ⁢                                    κ              ⁢                                                          ⁢              T                        q                    ⁢                      ln            ⁡                          (                                                I                                      C                    ⁢                                                                                  ⁢                    1                                                                    I                                      C                    ⁢                                                                                  ⁢                    2                                                              )                                                          (        1        )            where η is a non-ideality constant substantially equivalent to 1.00 or slightly more/less, κ is the well known Boltzmann's constant, q is the electron charge, T is the temperature in Kelvin, IC1 is a first collector current, and IC2 is a second collector current that are present at the measurement of a first base-emitter voltage and a second base-emitter voltage.
The classic diode equation is often employed to determine the actual temperature at a remotely located p-n-p transistor based on a ratio of approximated collector currents. In the past, since a ratio of collector currents tended to be relatively equivalent to a ratio of known emitter currents (IE), the diode equation could be accurately approximated in a rewritten form that follows:
                              T          =                                    Δ              ⁢                                                          ⁢                              V                BE                                                    η              ⁢                              κ                q                            ⁢                              ln                ⁡                                  (                                                            I                                              E                        ⁢                                                                                                  ⁢                        1                                                                                    I                                              E                        ⁢                                                                                                  ⁢                        2                                                                              )                                                                    ;                              where            ⁢                                                  ⁢                                          I                                  C                  ⁢                                                                          ⁢                  1                                                            I                                  C                  ⁢                                                                          ⁢                  2                                                              =                                    I                              E                ⁢                                                                  ⁢                1                                                    I                              E                ⁢                                                                  ⁢                2                                                                        (        2        )            
However, due in part to process variations for integrated circuits with smaller process geometries, the assumption regarding relatively equivalent ratios may no longer be valid. The beta (ratio of collector current over base current) has been shown to vary as much as ten percent or more between two known emitter currents for p-n-p transistors in integrated circuits manufactured from relatively smaller process geometries. Thus, the diode equation approximation (Equation 2) regarding the ratios of collector and emitter currents for a transistor can cause relatively inaccurate temperature measurements in an integrated circuit based on smaller process geometries. Relatively significant inaccurate temperature measurements can occur in integrated circuits that have process geometries of 90 nanometers or less. It should be appreciated that these measurements represent examples of problems experienced, and different manufacturers may start showing these effects at different process geometries.
Subsequent art provided for a more accurate temperature measurement for a transistor with a rewritten form of the diode equation (Equation 3) that provides for actually measuring or controlling the ratio of collector currents instead of the ratio of emitter currents.
                    T        =                              Δ            ⁢                                                  ⁢                          V              BE                                            η            ⁢                          κ              q                        ⁢                          ln              ⁡                              (                                                      I                                          C                      ⁢                                                                                          ⁢                      1                                                                            I                                          C                      ⁢                                                                                          ⁢                      2                                                                      )                                                                        (        3        )            
The disadvantage of this method, however, was that it required measuring IC and converting it to a digital form in real-time, which, when done accurately, is extremely expensive.
Yet another alternative has been to drive the collector currents to a predetermined ratio, thus eliminating the need to measure the collector currents independently. Consequently, Equation 3 can be rewritten as:
                    T        =                              Δ            ⁢                                                  ⁢                          V              BE                                            η            ⁢                                          κ                ⁢                                                                              q                        ⁢            ln            ⁢                                                  ⁢            N                                              (        4        )            
However, many temperature-sensing circuits use op-amps, which introduce offset voltages that adversely affect the target current ratio by causing error currents. Taking the offset into account, the current ratio can be expressed as:
                                          I            CN                                I                          C              ⁢                                                          ⁢              1                                      =                                            I              CTN                        +                                          V                OS                            R                                                          I                              CT                ⁢                                                                  ⁢                1                                      +                                          V                OS                            R                                                          (        5        )            Where ICT1 and ICTN are the actual currents injected into the circuit such that ICTN is N times the current ICT1, and R is the value of a the resistance seen by an input of the op-amp.
One solution to this problem is to multiplex between a high-current resistor (RN) and a low-current resistor (R1), where the value of the low-current resistor is N times the value of the high-current resistor. Thus, the equation for the current ratio becomes:
                                          I            CN                                I                          C              ⁢                                                          ⁢              1                                      =                                                            I                CTN                            +                                                V                  OS                                                  R                  N                                                                                    I                                  CT                  ⁢                                                                          ⁢                  1                                            +                                                V                  OS                                                  R                  1                                                              =          N                                    (        6        )            
Due to non-idealities in the resistance of two statistically independent resistors, however, an error factor still appears in the observed ration. In other words, the actual resistances of the resistors may be mismatched.